Solution of Large Systems of Equations Using Approximate Dynamic Programming Methods

Abstract

Abstract We consider fixed point equations, and approximation of the solution by projection on a low-dimensional subspace. We propose stochastic iterative algorithms, based on simulation, which converge to the approximate solution and are suitable for large-dimensional problems. We focus primarily on general linear systems and propose extensions of recent approximate dynamic programming methods, based on the use of temporal differences, which solve a projected form of Bellman’s equation by using simulation-based approximations to this equation, or by using a projected value iteration method.